隨著蓬勃發展的塑膠光電產業，塑膠光學鏡片具輕、薄、耐衝擊及可撓曲的優勢下逐步取代了玻璃鏡片，佔據了國內外大部分的市場，光學鏡片的產品品質被嚴苛的要求，但由於硬度低，耐磨損性較差，必需在其表面加工強硬膜層，以達到耐衝擊、抗磨損之效果。
本研究探討光學塑膠鏡片的表面精度與強化製程條件間的關係，結合了柏拉圖最佳解的概念和渴望函數來處理多目標實驗設計的問題，同時考量成本因素與有限制的實驗次數，找出一個近似D-optimal的實驗設計，並依此就光學塑膠鏡片強化工程來進行實驗並且分析，根據實驗結果找出位在柏拉圖前緣上的設計點，計算出未執行實驗的設計點之反應變數預測值後再更新柏拉圖前緣上的設計點，並透過渴望函數進行反應變數的轉換，最終考量製造成本，以效用成本比最大作為最佳設計點。並以實例來驗證本研究方法，討論變異數-共變異數矩陣對前緣的影響。預期在考量製造成本的多目標實驗設計下，實驗結果能提供決策者一個較為彈性的最佳解集合，提高決策者對品質特性預測上的準確性和可信度。

Plastic optical lenses replace the glass lens gradually with the rapid development of plastic photovoltaic industry, and occupy most of the global markets.Optical lenses product quality is required strictly.To achieve impact resistance and anti-wear effect, plastic optical lenses are required coatinghard film layers on its surface because of the low hardness and poor wear resistance. This study is to investigate the relationship between the surface of plastic lenses and precision optics hard coating process conditions. This is a multiple response optimization problem.
This study combines the Pareto frontier, the desirability function,and cost factor to deal with multiple objective experimental designssubjected to a limited number of experiments.The design is approximated bya D-optimal algorithm. According to this design matrix, optical plastic lenses hard coating experiments were performed and analyzed. We thenidentify the design points ofPareto frontier,build approximating models of responses, and predict the responses of unexecuted design points. If fitted unexecuted design points are not dominated, we then addthem to thePareto frontier.Multiple objectives are converted to a value through desirability function and then divided by the manufacturing cost of each design points. An optimum design is the one with the maximum ratio. An optical plastic lens hard coating example is performed and presented. Our results provide decision makers a more flexible set of optimal solutions to improve the accuracy and reliability of the prediction.

摘要 I
致謝 V
表目錄 VIII
圖目錄 IX
第一章 緒論 1
1.1 研究背景與動機 1
1.2研究目的 2
1.3研究範圍與流程 3
第二章 文獻回顧 5
2.1光學塑膠鏡片 5
2.1.1光學塑膠鏡片加硬膜層的研究進展 6
2.2多目標問題 7
2.3多目標最佳化方法 10
2.3.1權重法 10
2.3.2拘束法 11
2.3.3混合式方法 12
2.4柏拉圖解 12
2.5多目標最佳化問題求解 13
2.6實驗設計中的成本類型 14
第三章 問題描述與研究方法 16
3.1光學塑膠鏡片強化工程製程介紹 16
3.1.1目標特性決定 18
3.1.2控制變數介紹 22
3.2研究方法 23
3.2.1模型假設 23
3.2.2研究方法設計 25
3.3研究流程小結 31
第四章 實驗設計與分析 33
4.1實驗設計 33
4.2實驗設計方法與執行 33
4.2.1問題假設與因子設定 33
4.2.2找出最適設計矩陣 34
4.2.3尋找柏拉圖前緣 36
4.2.4更新柏拉圖前緣 37
4.2.5選擇最佳設計點 41
4.3驗證實驗 45
4.4小結 48
第五章 結論與未來研究建議 49
5.1結論 49
5.2研究貢獻 49
5.3未來研究建議 49
參考文獻 51
中文文獻 51
英文文獻 51

中文文獻
潘姝吟(2005)，「應用柏拉圖式與使用者偏好的多目標基因演算法來解決產能批量問題－以光學鏡片產業為例」，國立高雄第一科技大學運籌管理研究所碩士論文。
簡仲廷(2014)，「考慮效用成本比最大化之限制條件下多目標實驗設計」，國立成功大學工業與資訊管理研究所碩士論文。
英文文獻
Alaeddini, A., Yang, K., Mao, H., Murat, A. and Ankenman, B. (2013). An adaptive
sequential experimentation methodology for expensive response surface
optimization–case study in traumatic brain injury Modeling.Quality Reliability Engineering International,30(6), pp.767-793.
Alaeddini, A., Yang, K. and Murat, A. (2013). ASRSM: A sequential experimental
design for response surface optimization. Quality Reliability Engineering
International, 29(2), pp. 241-258.
Allen, T. T., and Yu, L. (2002). Low-cost response surface methods from simulation
optimization. Quality Reliability Engineering International, 18(1), pp.5-17.
Arnouts, H., Goos, P., and Jones, B.(2010). Design and analysis of industrial strip-plot experiments. Quality Reliability Engineering International, 26(2),pp. 127-136.
Bera, S.,and Mukherjee,I. (2013). An integrated approach based on principal component and multivariate process capability for simultaneous optimization of location and dispersion for correlated multiple response problems. Quality Engineering, 25(3), 266-281.
Corley, H. (1980). A new scalar equivalence for Pareto optimization. Automatic Control, IEEE Transactions on, 25(4), 829-830.
Caillez, F., Pages, J. P. (1976). Introduction à l'analyse de données. Paris : SMASH .
Chang, S. (1997). An algorithm to generate near D-optimal designs for multiple
responses surface models. IIE transactions, 29(12), pp. 1073-1081.
Derringer, G., and Suich, R. (1980). Simultaneous optimization of several responses
variables. Journal of Quality Technology, 12(4), pp. 214-219.
Ding, R., Dennis K. J. Lin, and Wei, D.(2004).Dual-response surface optimization: a weighted MSE approach. QualityEngineering, Vol. 16, pp. 377-385.
Fedorov, V. V. (1972). Theory of optimal experiments, Academic Press, New York.
de Aguiar, P. F., Bourguignon, B., Khots, M. S., Massart, D. L., and Phan-Than-Luu, R. (1995). D-optimal designs.Chemometrics and Intelligent Laboratory Systems,30(2), pp. 199-210.
Gass, S., and Saaty, T. (1955). The computational algorithm for the parametric objective function. Naval Research Logistics Quarterly, 2(1‐2), 39-45.
Harrington, E. C. (1965). The desirability function.Industrial Quality Control, 21(10), pp.494-498.
Howe, R. L. (1983). Developments in plastic optics for projection telvision systems. Consumer Electronics, IEEE Transactions on, (1), 44-53.
Hajela, P., and Lin, C. Y.(1992). Genetic searchstrategies in multicriterion optimal design. Structural and MultidisciplinaryOptimization, Vol. 4, pp. 99-107.
Izraelevitz, A. M., Anderson-Cook, C. M., ＆ Hamada, M. S. (2011). Illustrating the
use of statistical experimental design and analysis for multiresponse prediction and optimization.Quality Engineering,23(3), 265-277.
Kunjur, A., and Krishnamurty,S. (1997). A robust multi-criteria optimization approach. Mech. Mach. Theory, Vol.32,pp.797-810.
Kasemann, R., Schmidt, H. K., ＆Wintrich, E. (1994).A new type of Sol-Gel-Derived Inorganic-Organic nanocomposite.In Materials Research Society Symposium Proceedings , Vol. 346, pp. 915-919.
Khuri, A.I., andCornell, L.A. (1987).Response surfaces – designs and analyses.
Marcel Dekker, New York.
Lu, L., and Anderson‐Cook, C. M. (2012). Balancing multiple criteria incorporating cost using pareto front optimization for split‐plot designed experiments. Quality and Reliability Engineering International, 30(1), 37-55.
Lu, L., Anderson-Cook, C. M., and Robinson, T. J.(2012). Optimization of designed
experiments based on multiple criteria utilizing a paretofrontier.Technometrics,
53(4), pp. 353-365.
Mao, M. and Danzart, M. (2008). How to select the best subset of factors maximizing
the quality of multi-responseoptimization.Quality Engineering, 20(1), pp.63-74.
Marler, R. T., and Arora, J. S. (2004).Survey of multi-objective optimization methods
for engineering. Structural and Multidisciplinary Optimization, 26(6), pp. 369-395.
Marglin, S. A. (1967). Public Investment Criteria.MIT Press.
Nakache, J. P., Confais, J. (2005). Approche pragmatique de la classification. Arbres hiérarchiques, partitionnements. Paris : Technip.
Ngatchou, P., Zarei, A., and El-Sharkawi, M. A. (2005).Pareto multi objective optimization.Proceedings of IEEE International Conference on Intelligent Systems Application to Power Systems, Arlington, VA, pp.84-91.
Ombuki, B., Ross, B. J., and Hanshar, F.(2006). Multi-objective genetic algorithms for vehicle routing problem with time windows. Applied Intelligence, Vol. 24, pp. 17–30.

Pal, S. and Gauri, Susanta Kumar. (2010). Multi-response optimization using multiple
regression-based weighted signal-to-noise ratio(MRWSN).Quality Engineering, 22(4), pp. 336-350.
Samson, F. (1996).Ophthalmic lens coatings.Surface and coatings technology, 81(1), pp.79-86.
Schottner, G., Rose, K., and Posset, U. (2003).Scratch and abrasion resistant coatings on plastic lenses-state of the art, current developments and perspectives. Journal of sol-gel science and technology, 27(1), pp.71-79.
Schaffer, J. D.(1985). Multiple objective optimization with vector evaluated genetic algorithms. in Proceeding of the First International Conference on Genetic Algorithm, pp.93-100.
Wendell, R. E., and Lee, D. N. (1977).Efficiency in multiple objective optimization problems. Mathematical Programming, 12(1), 406-414.
Zadeh,L.(1963).Optimality and non-scalar-valued performance criteria .IEEE Transactions on Automatic Control, 8:59-60.